Show that is a solution to this equation, and then solve the initial value problem.

hmm, how do you go about this one?

I thougt the solution would be on the form
since the solution to the homogenous equation

When a question is expressed like this you generally just show that the suggested solution is in fact a solution.

So put:

Then;

Then:

As required.

What this shows is that is a particular integral for this ODE. To find the solution to the IVP you now need only solve the homogeneous ODE add its general solution to the PI and apply the initial conditions.